Normal function: Difference between revisions
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* \(\alpha<\beta \Leftrightarrow f(\alpha)<f(\beta)\)
* \(f(\alpha)=\sup f(\beta)\) if and only if \(\beta<\alpha\) and \(\alpha\) is a [[limit ordinal]].
Veblen's fixed point lemma, which is essential for constructing the [[Veblen hierarchy]], guarantees that, not only does every normal function have a [[fixed point]], but the class of fixed points is unbounded and their enumeration function is also normal.
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